A student has a class with 4 tests, each worth 100 points, and has earned these scores on the first three: 75, 74, 71 what is her average now? what must she earn on the fourth test to get a B(80) in the class?

Question

-studywith- · Answer

Hi I can help.  If it's not too late.

oliviablehhh · Answer

Hi! So I already got the average of the 3 given numbers. Now I just need help with that they should earn on the 4th test in order to get a "B"

mww · Answer

Average of the four tests would be the sum of the four scores. 
Let the fourth score be X. 
The mean of the scores must give you 80 as you specified.
$$Mean_4= \frac{ 75 + 74 + 71 + X }{ 4 } = 80$$

Then simplify and solve for X.

Note: In some questions, instead of telling you what the first couple of scores are, they might give you the present mean of the scores instead. In that case to find the next score X that would give you a new mean you must use the relationship:

$$Mean_{n} = \frac{ Sum_{n} }{ n } \rightarrow  Sum_{n} = n \times Mean_{n}$$
Then new mean of n+1 scores is
$$Mean_{n+1} = \frac{ Sum_{n+1} }{ n+1 } = \frac{ Sum_{n} + X_{n+1} }{ n+1 } = \frac{ nMean_n + X }{ n+1}$$